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Absorption of sound and kinetic coefficients of elastic bodies
ANNALS OF PHYSICS
218, 197-198 (1992)
Abstracts
of Papers
to Appear
in Future
issues
of Sound and Kinetic CoefJcients qf Elastic Bodies. D. A. GARANIN AND V. S. LUTOVINOV. Moscow Institute of Radioengineering. Electronics, and Automation, 117454, Prospect Vernadskogo 78. Russia.
Absorption
The attenuation of the low frequency longitudinal and transverse sound waves in the isotropic elastic body is calculated in the framework of the diagrammatic Green’s function approach taking into account three-phonon and defect scattering processes. It is shown that the system of integral equations for the renormalized three-phonon confluence vertices is a generalization of the system of linearized Boltzmann equations for the phonon gas considered by Akhiezer. An accurate solution of these equations gives the microscopic expressions for the kinetic coeIIicients (first and second viscosities, heat conductivity) of the isotropic elastic media entering macroscopic formulae for the sound attenuation. Regularizarion and the Phase of One-Loop Determinants. D. G. C. M&EON. Department of Mathematical Physics, University College Galway, Galway, Ireland; AND T. N. SHERRY. School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4, Ireland.
Operator
Operator regularization is a symmetry preserving regularization procedure to all orders of ~rtur~tion theory that avoids explicit divergences. At one-loop order it is det H which is regularized, where H is an operator appearing in the theory. For some theories it is not possible to treat det H directly; in previous implementations det H has simply been replaced by det tH2 in such cases.However, if H has negative or imaginary eigenvalues then information about the phase of det H may be lost in this replacement. We discuss this general problem for an arbitrary operator H and we give a prescription for finding the phase of det H that reduces, if H is Hermitian, to the rl-function analysis introduced by Gilkey and further exploited by Witten and others. We consider explicitly one example of a non-He~itian operator and three examples of a Hermitian operator. To illustrate how we treat the phase of the dete~inant of a non-He~itian operator, we consider the determinant associated with a spinor coupled to an external axial vector field and show how the phase of this determinant is associated with the axial anomaly, using a technique introduced by Bukhbinder, Gusynin, and Fomin. In three-dimensional quantum electrodynamics (or, more generally, its non-abelian analogue) the q-function can be computed exactly (following Birmingham, Cho, Kantowski, and Rakowski) when there is an external vector field, showing that an effective Chem-Simons action is generated, resulting in a quantization of the gauge coupling constant. In the final two examples H is a super-operator, spanning a space containing both bosons and fermions. We compute the contribution of the two-point spinor function to the q-function when the vector field to which the spinor couples has a Chern-Simons action; it simply serves to renormalize the coefficient of the kinetic term for the spinor field. Finally, we consider the self-energy in a two-dimensional model in which a Majorana spinor couples to a vector field which has a topological action. In this case the q-function vanishes, but the c-function indicates that chiral symmetry is broken despite the fact that all the unregulated Feynman diagrams in this model vanish.
Simultaneous
Measurement
of Conjugate
Variables.
STIG STENHOLM.
Research Institute for Theoretical
Physics, Siltavuorenpenger 20 C, SF-00170 Helsinki, Finland. This paper investigates the possibility of extracting optimum information about the momentum and position variables of a quantum mechanical system. For the observation we use a pair of independent detectors, which contribute their own noise to the recorded result. In the optimal case the setup measures the Q-distribution leading to antinormally ordered expectation values. The class of initial detector states
197 0003-4916/92 $9.00 0 1992 by Academic ties% Inc. All rights of reproduction in any fwm reserved. Copyright
218, 197-198 (1992)
Abstracts
of Papers
to Appear
in Future
issues
of Sound and Kinetic CoefJcients qf Elastic Bodies. D. A. GARANIN AND V. S. LUTOVINOV. Moscow Institute of Radioengineering. Electronics, and Automation, 117454, Prospect Vernadskogo 78. Russia.
Absorption
The attenuation of the low frequency longitudinal and transverse sound waves in the isotropic elastic body is calculated in the framework of the diagrammatic Green’s function approach taking into account three-phonon and defect scattering processes. It is shown that the system of integral equations for the renormalized three-phonon confluence vertices is a generalization of the system of linearized Boltzmann equations for the phonon gas considered by Akhiezer. An accurate solution of these equations gives the microscopic expressions for the kinetic coeIIicients (first and second viscosities, heat conductivity) of the isotropic elastic media entering macroscopic formulae for the sound attenuation. Regularizarion and the Phase of One-Loop Determinants. D. G. C. M&EON. Department of Mathematical Physics, University College Galway, Galway, Ireland; AND T. N. SHERRY. School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4, Ireland.
Operator
Operator regularization is a symmetry preserving regularization procedure to all orders of ~rtur~tion theory that avoids explicit divergences. At one-loop order it is det H which is regularized, where H is an operator appearing in the theory. For some theories it is not possible to treat det H directly; in previous implementations det H has simply been replaced by det tH2 in such cases.However, if H has negative or imaginary eigenvalues then information about the phase of det H may be lost in this replacement. We discuss this general problem for an arbitrary operator H and we give a prescription for finding the phase of det H that reduces, if H is Hermitian, to the rl-function analysis introduced by Gilkey and further exploited by Witten and others. We consider explicitly one example of a non-He~itian operator and three examples of a Hermitian operator. To illustrate how we treat the phase of the dete~inant of a non-He~itian operator, we consider the determinant associated with a spinor coupled to an external axial vector field and show how the phase of this determinant is associated with the axial anomaly, using a technique introduced by Bukhbinder, Gusynin, and Fomin. In three-dimensional quantum electrodynamics (or, more generally, its non-abelian analogue) the q-function can be computed exactly (following Birmingham, Cho, Kantowski, and Rakowski) when there is an external vector field, showing that an effective Chem-Simons action is generated, resulting in a quantization of the gauge coupling constant. In the final two examples H is a super-operator, spanning a space containing both bosons and fermions. We compute the contribution of the two-point spinor function to the q-function when the vector field to which the spinor couples has a Chern-Simons action; it simply serves to renormalize the coefficient of the kinetic term for the spinor field. Finally, we consider the self-energy in a two-dimensional model in which a Majorana spinor couples to a vector field which has a topological action. In this case the q-function vanishes, but the c-function indicates that chiral symmetry is broken despite the fact that all the unregulated Feynman diagrams in this model vanish.
Simultaneous
Measurement
of Conjugate
Variables.
STIG STENHOLM.
Research Institute for Theoretical
Physics, Siltavuorenpenger 20 C, SF-00170 Helsinki, Finland. This paper investigates the possibility of extracting optimum information about the momentum and position variables of a quantum mechanical system. For the observation we use a pair of independent detectors, which contribute their own noise to the recorded result. In the optimal case the setup measures the Q-distribution leading to antinormally ordered expectation values. The class of initial detector states
197 0003-4916/92 $9.00 0 1992 by Academic ties% Inc. All rights of reproduction in any fwm reserved. Copyright